pseudohyperbolic equation
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scholarly journals PROBLEM WITH NONLOCAL INTEGRAL CONDITION FOR PSEUDOHYPERBOLIC EQUATION OF THE FOURTH-ORDER

2017 ◽  
Vol 20 (3) ◽  
pp. 46-55
Author(s):  
S.V. Kirichenko
Keyword(s):  
Fourth Order ◽  
Existence And Uniqueness ◽  
Integral Condition ◽  
Generalized Solution ◽  
Pseudohyperbolic Equation ◽  
Nonlocal Integral Condition

In this article, we study a problem for a multimensional pseudohyperbolic equation of the fourth-order with an integral condition. Existence and uniqueness of a generalized solution is proved.

scholarly journals Problem on vibration of a bar with nonlinearsecond-order boundary damping

2017 ◽  
Vol 21 (3) ◽  
pp. 9-20
Author(s):  
A.B. Beylin ◽  
L.S. Pulkina
Keyword(s):  
A Priori Estimates ◽  
Longitudinal Vibration ◽  
A Priori ◽  
Initial Boundary ◽  
Generalized Solution ◽  
Application Form ◽  
Boundary Damping ◽  
Initial Boundary Problem ◽  
Priori Estimates ◽  
Pseudohyperbolic Equation

In this paper, we study the initial-boundary problem with nonlinear dynam- ical boundary condition for the pseudohyperbolic equation. This problem repre- sents a mathematical model of longitudinal vibration in a thick short bar with dynamic nonlinear second-order boundary damping. The existence and unique- ness of a generalized solution are proved. The proof is based on a priori estimates and Galerkin procedure. This approach allows to construct approximation in the suitable for practical application form.

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